Results of nested canalizing functions
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Boolean nested canalizing functions (NCF) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study the certificate complexity of NCF. We obtain the formula for b - certificate complexity, C_0(f) and C_1(f). Consequently, we get a direct proof of the certificate complexity formula of NCF. Symmetry is another interesting property of Boolean functions. We significantly simplify the proofs of some recent theorems about partial symmetry of NCF. We also describe the algebraic normal form of the s-symmetric nested canalizing functions. We obtain the general formula of the cardinality of the set of all n-variable s-symmetric Boolean NCF for s=1,...,n. Particularly, we obtained the cardinality formula for the set of all the strongly asymmetric Boolean NCFs.
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